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A079628
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Array of coefficients of P(n,x) = det (M(n,x)) where M(n,x) is the n X n matrix m(i,j)=x if i>j m(i,j)=1-x if i<=j.
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4
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1, 1, -1, 1, -3, 2, 1, -5, 8, -4, 1, -7, 18, -20, 8, 1, -9, 32, -56, 48, -16, 1, -11, 50, -120, 160, -112, 32, 1, -13, 72, -220, 400, -432, 256, -64, 1, -15, 98, -364, 840, -1232, 1120, -576, 128, 1, -17, 128, -560, 1568, -2912, 3584, -2816, 1280, -256, 1, -19, 162, -816, 2688, -6048, 9408, -9984, 6912, -2816, 512, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Formatted as a triangular array, this is [1, 0, 0, 0, 0, 0, 0, ...] DELTA [ -1, -1, 0, 0, 0, 0, 0, 0, ...] (see construction in A084938) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Aug 09 2005
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FORMULA
| P(n, x)= (-1)^n*(x-1)*(2*x-1)^(n-1).
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EXAMPLE
| det(M(4,x))=1-7x+18x^2-20x^3+8x^4.
1;
1,-1;
1,-3,2;
1,-5,8,-4;
1,-7,18,-20,8;
1,-9,32,-56,48,-16;
1,-11,50,-120,160,-112,32;
1,-13,72,-220,400,-432,256,-64;
1,-15,98,-364,840,-1232,1120,-576,128;
1,-17,128,-560,1568,-2912,3584,-2816,1280,-256,
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MAPLE
| A079628 := proc(n, k) local x; expand((-1)^n* (x-1)*(2*x-1)^(n-1)) ; coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, Nov 04 2011
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CROSSREFS
| Cf. A081277.
Cf. A167580 and A167591 - Johannes W. Meijer (meijgia(AT)hotmail.com), Nov 23 2009
Sequence in context: A073370 A129675 A081277 * A140287 A077951 A077976
Adjacent sequences: A079625 A079626 A079627 * A079629 A079630 A079631
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KEYWORD
| sign,tabl
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 30 2003
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EXTENSIONS
| Sign added to formula. - R. J. Mathar, Nov 04 2011
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